If you want to get into basics, there are vessels which serve commerce; transporting goods, trade, et cetera. There are warships. There are fishermen. There are survey ships, cable-laying ships, all manner of vessels. But the term "merchantman" refers, generally, to ships engaged in carrying cargo for trade or sale. Many today are 'container ships' carrying their cargoes in containers below and on the upper deck. Then there are your bulk ore carriers, fuel tankers and the like. These last three categories probably make up the majority of the larger ships plying the oceans today.
But probably the most numerous types would be the fishing boats. Though not generally referred to a merchant ships, they are, in many instances run by business and strictly speaking, could also be classified as merchants.